Category: Integration

Question Number 24817 by A1B1C1D1 last updated on 26/Nov/17 Answered by mrW1 last updated on 26/Nov/17 $$=\int_{\mathrm{0}} ^{\:\mathrm{4}} \left[\frac{\mathrm{1}}{\mathrm{2}}\left({y}−\frac{{y}^{\mathrm{2}} }{\mathrm{16}}\right)+{y}\left(\sqrt{{y}}−\frac{{y}}{\mathrm{4}}\right)\right]{dy} \\ $$$$=\int_{\mathrm{0}} ^{\:\mathrm{4}} \left(\frac{{y}}{\mathrm{2}}−\frac{\mathrm{9}{y}^{\mathrm{2}} }{\mathrm{32}}+{y}^{\frac{\mathrm{3}}{\mathrm{2}}}…

Question Number 155883 by john_santu last updated on 05/Oct/21 $$\int\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} {x}}\:{dx}=? \\ $$ Commented by aliyn last updated on 05/Oct/21 $$\boldsymbol{{I}}\:=\:\int\:\frac{\boldsymbol{{tan}}^{\mathrm{2}} \boldsymbol{{x}}}{\mathrm{1}\:−\:\boldsymbol{{tan}}^{\mathrm{2}} \boldsymbol{{x}}}\:\boldsymbol{{dx}} \\…

Question Number 90321 by M±th+et£s last updated on 22/Apr/20 $$\int\frac{\mathrm{1}}{{x}\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}^{\mathrm{5}} }}{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{1}}{{sin}^{\mathrm{2}} \left({x}\right)+\mathrm{5}{sin}\left({x}\right)+\mathrm{6}}{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{2}{z}−\mathrm{5}}{\mathrm{4}{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{5}}{dz} \\ $$$$ \\ $$$$\int{sec}^{\mathrm{5}}…

Question Number 90292 by mathmax by abdo last updated on 22/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{e}^{{zx}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx}\:{with}\:{z}\:{from}\:{C}\:{and}\:{Re}\left({z}\right)<\mathrm{0} \\ $$ Commented by mathmax by abdo last…

Question Number 90279 by mathmax by abdo last updated on 22/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}\:{dx} \\ $$ Commented by mathmax by abdo last updated…